Are there any conferences dedicated to artificial general intelligence?
There are several conferences dedicated to AGI or human-level intelligence, such as

AGI Conferences (organized by AGI society)
Biologically Inspired Cognitive Architectures (organized by BICA Society)
Advances in Cognitive Systems
IEEE Task Force on Towards Human-like Intelligence

The conferences focus on topics such as cognitive architectures, autonomy, creativity, lifelong learning, and formal models of general intelligence. There are also journals associated with these conferences (see [1], [2], [3]). If you want to know more about them, I suggest that you go to their websites.